P varies jointly as m and u, and varies inversely as q. Given that p = 4, m = 3 and u = 2 and q = 1, find the value of p when m = 6, u = 4 and q =85

P varies jointly as m and u, and varies inversely as q. Given that p = 4, m = 3 and u = 2 and q = 1, find the value of p when m = 6, u = 4 and q =$\frac{8}{5}$

Answer Details

P $\propto$ mu, p $\propto \frac{1}{q}$
p = muk ................ (1)
p = $\frac{1}{q}k$.... (2)
Combining (1) and (2), we get
P = $\frac{mu}{q}k$
4 = $\frac{m\times u}{1}k$
giving k = $\frac{4}{6}=\frac{2}{3}$
So, P = $\frac{mu}{q}\times \frac{2}{3}=\frac{2mu}{3q}$
Hence, P = $\frac{2\times 6\times 4}{3\times \frac{8}{5}}$
P = $\frac{2\times 6\times 4\times 5}{3\times 8}$
p = 10